Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 2
Chapter 2 of 31

Simplification (BODMAS)

The correct order of operations for solving multi-step arithmetic expressions without error.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

BODMAS Rule

Order of operations for simplifying an expression:

LetterOperation
BBrackets — solved in order: ( ), { }, [ ]
OOf (meaning multiplication, e.g. "½ of 20")
DDivision
MMultiplication
AAddition
SSubtraction

Bracket Solving Order

  • Solve innermost bracket first: ( ) → then { } → then [ ]
  • A minus sign directly before a bracket flips the sign of every term inside when removed

Common Simplification Traps

  • "Of" is calculated BEFORE division/multiplication when it appears alongside them in the same expression
  • Division and Multiplication have equal priority — solve strictly left to right between them
  • Addition and Subtraction have equal priority — solve strictly left to right between them
💡 Example: 20 − 4 of 3 + 6 ÷ 2 = 20 − 12 + 3 = 11 (Of first, then division, then left-to-right addition/subtraction)

VBODMAS (with Virnaculum/Bar)

When a horizontal bar (vinculum) appears over an expression (like a fraction line), solve everything under the bar first — before applying BODMAS to the rest.

💡 Squares to memorise: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49, 8²=64, 9²=81, 10²=100, 11²=121, 12²=144, 13²=169, 14²=196, 15²=225, 20²=400, 25²=625

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